Publication Detail

Cut Locus and Medial Axis in Global Shape Interrogation and Representation

Franz-Erich Wolter
44 pp.
MITSG 93-11

Although there exists extensive literature on the Medial Axis Transform (MAT) which discusses mainly computional methods, basic global and even basic local aspects of the MAT concept are not sufficiently well understood. Until now, the research activities performed in the whole MAT area have mainly focussed on computational techniques, and one misses a systematical foundational investigation of the concept as a whole. One of the main goals of this paper is to help fill this gap, and also to supply a systematic analysis of the above mentioned topological properties. The MAT concept's relation to the concepts of cut loci, equidistantial sets, and Voronoi diagrams is investigated; it is shown that the cut locus concept offers a common framework lucidly unifying different but related concepts such as Voronoi diagrams, equidistantial sets and medial axes. The distance function and its differentiability properties play a crucial role for many considerations in this paper.

type: Technical reports

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